#include "wombats.h"
#include <bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
using namespace std;
const int nx=5e3+5, cx=2e2+5, kx=5, inf=1e9;
int r, c, ver[nx][cx], qs[nx][cx], dp[2][cx][cx], opt[cx][cx];
int dist(int row, int a, int b)
{
    if (b>=a) return ver[row][a]+qs[row][b]-qs[row][a];
    else return ver[row][a]+qs[row][a]-qs[row][b];
}
struct segtree
{
    struct matrix
    {
        int mat[cx][cx];
        matrix()
        {
            for (int i=0; i<c; i++) for (int j=0; j<c ;j++) mat[i][j]=inf;
        }
    } d[2050];
    matrix mul(matrix &lhs, matrix &rhs)
    {
        matrix res;
        for (int i=c-1; i>=0; i--)
        {
            for (int j=0; j<=c-1; j++)
            {
                int l=(j!=0)?opt[i][j-1]:0, r=(i!=c-1)?opt[i+1][j]:c-1;
                for (int k=l; k<=r; k++) if (lhs.mat[i][k]+rhs.mat[k][j]<res.mat[i][j]) res.mat[i][j]=lhs.mat[i][k]+rhs.mat[k][j], opt[i][j]=k;
            }
        }
        return res;
    }
    matrix construct(int l, int r)
    {
        matrix res;
        for (int i=0; i<c; i++) for (int j=0; j<c; j++) res.mat[i][j]=dist(l, i, j);
        for (int i=l+1; i<=r; i++)
        {
            matrix nxt;
            for (int j=0; j<c ;j++) for (int k=0; k<c; k++) nxt.mat[j][k]=dist(i, j, k);
            res=mul(res, nxt);
        }
        return res;
    }
    void build(int l, int r, int i)
    {
        if (r-l+1<=kx) return d[i]=construct(l, r), void();
        int md=(l+r)/2;
        build(l, md, 2*i);
        build(md+1, r, 2*i+1);
        d[i]=mul(d[2*i], d[2*i+1]);
    }
    void update(int l, int r, int i, int idx)
    {
        if (idx<l||r<idx) return;
        if (r-l+1<=kx) return d[i]=construct(l, r), void();
        int md=(l+r)/2;
        update(l, md, 2*i, idx);
        update(md+1, r, 2*i+1, idx);
        d[i]=mul(d[2*i], d[2*i+1]);
    }
} s;
void init(int R, int C, int H[5000][200], int V[5000][200]) {
    r=R, c=C;
    for (int i=0; i<R-1; i++) for (int j=0; j<C; j++) ver[i+1][j]=V[i][j];
    for (int i=0; i<R; i++) for (int j=0; j<C-1; j++) qs[i][j+1]=H[i][j]+qs[i][j];
    s.build(1, r-1, 1);
}
void changeH(int P, int Q, int W) {
    int lst=qs[P][Q+1]-qs[P][Q];
    int delta=W-lst;
    for (int i=Q+1; i<c; i++) qs[P][i]+=delta;
    if (P>0) s.update(1, r-1, 1, P);
}
void changeV(int P, int Q, int W) {
    ver[P+1][Q]=W;
    s.update(1, r-1, 1, P+1);
}
int escape(int V1, int V2) {
    vector<int> tmp;
    int res=1e9;
    for (int i=0; i<c; i++) res=min(res, s.d[1].mat[i][V2]+dist(0, V1, i));
    return res;
}
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